Center for Discrete Mathematics and Theoretical Computer Science

The recent FCC frequency allocation for UWB has generated a lot of interest in UWB technologies. There is 7,500 MHz of spectrum for unlicensed use. The main limitations are provided by the low-power spectral density and by the fact that the transmit signal must occupy at least 500 MHz at whole times. IEEE 802.15.3a is being developed for high-bit-rate PAN applications, and UWB is the most promising technology to support the stringent requirements: 110, 200, and 480 Mb/s. Two UWB multiband systems, frequency hopping and Spectral Keying, have been described in this article. Both systems meet the stringent requirements provided by IEEE 802.15.

The main theme of this book is the interplay between the behaviour of a class of stochastic processes (random walks) and discrete structure theory. The author considers Markov chains whose state space is equipped with the structure of an infinite, locally finite graph, or as a particular case, of a finitely generated group. The transition probabilities are assumed to be adapted to the underlying structure in some way that must be specified precisely in each case. From the probabilistic viewpoint, the question is what impact the particular type of structure has on various aspects of the behaviour of the random walk. Vice-versa, random walks may also be seen as useful tools for classifying, or at least describing the structure of graphs and groups. Links with spectral theory and discrete potential theory are also discussed. This book will be essential reading for all researchers working in stochastic process and related topics

Logistic regression analysis of high-dimensional data, such as natural language text, poses computational and statistical challenges. Maximum likelihood estimation often fails in these applications. We present a simple Bayesian logistic regression approach that uses a Laplace prior to avoid overfitting and produces sparse predictive models for text data. We apply this approach to a range of document classification problems and show that it produces compact predictive models at least as effective as those produced by support vector machine classifiers or ridge logistic regression combined with feature selection. We describe our model fitting algorithm, our open source implementations (BBR and BMR), and experimental results.

We present the design of a superconducting qubit that has circulating currents of opposite sign as its two states. The circuit consists of three nanoscale aluminum Josephson junctions connected in a superconducting loop and controlled by magnetic fields. The advantages of this qubit are that it can be made insensitive to background charges in the substrate, the flux in the two states can be detected with a superconducting quantum interference device, and the states can be manipulated with magnetic fields. Coupled systems of qubits are also discussed as well as sources of decoherence.

Stefan Brands proposes cryptographic building blocks for the design of digital certificates that preserve privacy without sacrificing security. As paper-based communication and transaction mechanisms are replaced by automated ones, traditional forms of security such as photographs and handwritten signatures are becoming outdated. Most security experts believe that digital certificates offer the best technology for safeguarding electronic communications. They are already widely used for authenticating and encrypting email and software, and eventually will be built into any device or piece of software that must be able to communicate securely. There is a serious problem, however, with this unavoidable trend: unless drastic measures are taken, everyone will be forced to communicate via what will be the most pervasive electronic surveillance tool ever built. There will also be abundant opportunity for misuse of digital certificates by hackers, unscrupulous employees, government agencies, financial institutions, insurance companies, and so on.In this book Stefan Brands proposes cryptographic building blocks for the design of digital certificates that preserve privacy without sacrificing security. Such certificates function in much the same way as cinema tickets or subway tokens: anyone can establish their validity and the data they specify, but no more than that. Furthermore, different actions by the same person cannot be linked. Certificate holders have control over what information is disclosed, and to whom. Subsets of the proposed cryptographic building blocks can be used in combination, allowing a cookbook approach to the design of public key infrastructures. Potential applications include electronic cash, electronic postage, digital rights management, pseudonyms for online chat rooms, health care information storage, electronic voting, and even electronic gambling.

We address optimization problems in which we are given contradictory pieces of input information and the goal is to find a globally consistent solution that minimizes the extent of disagreement with the respective inputs. Specifically, the problems we address are rank aggregation, the feedback arc set problem on tournaments, and correlation and consensus clustering. We show that for all these problems (and various weighted versions of them), we can obtain improved approximation factors using essentially the same remarkably simple algorithm. Additionally, we almost settle a long-standing conjecture of Bang-Jensen and Thomassen and show that unless NP⊆BPP, there is no polynomial time algorithm for the problem of minimum feedback arc set in tournaments.

This paper presents new graph-theoretic results appropriate for the analysis of a variety of consensus problems cast in dynamically changing environments. The concepts of rooted, strongly rooted, and neighbor-shared are defined, and conditions are derived for compositions of sequences of directed graphs to be of these types. The graph of a stochastic matrix is defined, and it is shown that under certain conditions the graph of a Sarymsakov matrix and a rooted graph are one and the same. As an illustration of the use of the concepts developed in this paper, graph-theoretic conditions are obtained which address the convergence question for the leaderless version of the widely studied Vicsek consensus problem.

A feedback vertex set of a graph is a subset of vertices that contains at least one vertex from every cycle in the graph. The problem considered is that of finding a minimum feedback vertex set given a weighted and undirected graph. We present a simple and efficient approximation algorithm with performance ratio of at most 2, improving previous best bounds for either weighted or unweighted cases of the problem. Any further improvement on this bound, matching the best constant factor known for the vertex cover problem, is deemed challenging. The approximation principle, underlying the algorithm, is based on a generalized form of the classical local ratio theorem, originally developed for approximation of the vertex cover problem, and a more flexible style of its application.

Ultrasound (US) elasticity imaging is an extension of the ancient art of palpation and of earlier US methods for viewing tissue stiffness such as echopalpation. Elasticity images consist of either an image of strain in response to force or an image of estimated elastic modulus. There are 3 main types of US elasticity imaging: elastography that tracks tissue movement during compression to obtain an estimate of strain, sonoelastography that uses color Doppler to generate an image of tissue movement in response to external vibrations, and tracking of shear wave propagation through tissue to obtain the elastic modulus. Other modalities may be used for elasticity imaging, the most powerful being magnetic resonance elastography. With 4 commercial US scanners already offering elastography and more to follow, US-based methods may be the most widely used for the near future. Elasticity imaging is possible for nearly every tissue. Breast mass elastography has potential for enhancing the specificity of US and mammography for cancer detection. Lesions in the thyroid, prostate gland, pancreas, and lymph nodes have been successfully imaged using elastography. Evaluation of diffuse disease including cirrhosis and transplant rejection is also possible using both imaging and nonimaging methods. Vascular imaging including myocardium, blood vessel wall, plaque, and venous thrombi has also shown great potential. Elasticity imaging may also be important in assessing the progress of ablation therapy. Recent work in assessing porous materials using elastography suggests that the technique may be useful in monitoring the severity of lymphedema.

OBJECTIVE: To update and examine national temporal trends in contralateral prophylactic mastectomy (CPM) and determine whether survival differed for invasive breast cancer patients based on hormone receptor (HR) status and age. METHODS: We identified women diagnosed with unilateral stage I to III breast cancer between 1998 and 2012 within the Surveillance, Epidemiology, and End Results registry. We compared characteristics and temporal trends between patients undergoing breast-conserving surgery, unilateral mastectomy, and CPM. We then performed Cox proportional-hazards regression to examine breast cancer-specific survival (BCSS) and overall survival (OS) in women diagnosed between 1998 and 2007, who underwent breast-conserving surgery with radiation (breast-conserving therapy), unilateral mastectomy, or CPM, with subsequent subgroup analysis stratifying by age and HR status. RESULTS: Of 496,488 women diagnosed with unilateral invasive breast cancer, 59.6% underwent breast-conserving surgery, 33.4% underwent unilateral mastectomy, and 7.0% underwent CPM. Overall, the proportion of women undergoing CPM increased from 3.9% in 2002 to 12.7% in 2012 (P < 0.001). Reconstructive surgery was performed in 48.3% of CPM patients compared with only 16.0% of unilateral mastectomy patients, with rates of reconstruction with CPM rising from 35.3% in 2002 to 55.4% in 2012 (P < 0.001). When compared with breast-conserving therapy, we found no significant improvement in BCSS or OS for women undergoing CPM (BCSS: HR 1.08, 95% confidence interval 1.01-1.16; OS: HR 1.08, 95% confidence interval 1.03-1.14), regardless of HR status or age. CONCLUSIONS: The use of CPM more than tripled during the study period despite evidence suggesting no survival benefit over breast conservation. Further examination on how to optimally counsel women about surgical options is warranted.

Given a high dimensional convex body K⊆ℝn by a separation oracle, we can approximate its volume with relative error ε, using O*(n5) oracle calls. Our algorithm also brings the body into isotropic position. As all previous randomized volume algorithms, we use “rounding” followed by a multiphase Monte-Carlo (product estimator) technique. Both parts rely on sampling (generating random points in K), which is done by random walk. Our algorithm introduces three new ideas: the use of the isotropic position (or at least an approximation of it) for rounding; the separation of global obstructions (diameter) and local obstructions (boundary problems) for fast mixing; and a stepwise interlacing of rounding and sampling. © 1997 John Wiley & Sons, Inc. Random Struct. Alg., 11, 1–50, 1997

Abstract Control rules governing transciption of eukaryotic genes can be modeled as Boolean function, and these rules are strongly biased toward large numbers of “canalizing” inputs. The ensemble of networks with the observed canalizing bias predicts cells are in an ordered regime with convergent flow in transcription state space, a percolating subnetwork of genes fixed on or off an isolated islands of twinkling genes turning on or off, and a near power‐law distribution of cascades of gene activity changes following perturbations. The data suggest that a given cell state or type can be represented as an attractor of transcriptional activity or flow over time. © 2002 Wiley Periodicals, Inc.

A computational method has been developed for the assignment of a protein sequence to a folding class in the Structural Classification of Proteins (SCOP). This method uses global descriptors of a primary protein sequence in terms of the physical, chemical, and structural properties of the constituent amino acids. Neural networks are utilized to combine these descriptors in a way to discriminate members of a given fold from members of all other folds. An extensive testing of the method has been performed to evaluate its prediction accuracy. The method is applicable for the fold assignment of any protein sequence with or without significant sequence homology to known proteins. A WWW page for predicting protein folds is available at URL http://cbcg.lbl.gov/. Proteins 1999;35:401–407.

A new scalable modeling framework and scalable parallel simulations make it possible to analyze the detailed behaviour of large, multidomain multiprotocol Internet models. The article focuses on simulation research. It describes the software designs that let us construct and run appropriately large models. After several years of research, we have developed a scalable network modeling framework, a scalable simulation framework (SSF), and scalable parallel discrete event simulators capable of modeling the Internet at unprecedented scales.

Given an arc-weighted directed graph G = (V, A, /spl lscr/) and a pair of nodes s, t, we seek to find an s-t walk of length at most B that maximizes some given function f of the set of nodes visited by the walk. The simplest case is when we seek to maximize the number of nodes visited: this is called the orienteering problem. Our main result is a quasi-polynomial time algorithm that yields an O(log OPT) approximation for this problem when f is a given submodular set function. We then extend it to the case when a node v is counted as visited only if the walk reaches v in its time window [R(v), D(v)]. We apply the algorithm to obtain several new results. First, we obtain an O(log OPT) approximation for a generalization of the orienteering problem in which the profit for visiting each node may vary arbitrarily with time. This captures the time window problem considered earlier for which, even in undirected graphs, the best approximation ratio known [Bansal, N et al. (2004)] is O(log/sup 2/ OPT). The second application is an O(log/sup 2/ k) approximation for the k-TSP problem in directed graphs (satisfying asymmetric triangle inequality). This is the first non-trivial approximation algorithm for this problem. The third application is an O(log/sup 2/ k) approximation (in quasi-poly time) for the group Steiner problem in undirected graphs where k is the number of groups. This improves earlier ratios (Garg, N et al.) by a logarithmic factor and almost matches the inapproximability threshold on trees (Halperin and Krauthgamer, 2003). This connection to group Steiner trees also enables us to prove that the problem we consider is hard to approximate to a ratio better than /spl Omega/(log/sup 1-/spl epsi// OPT), even in undirected graphs. Even though our algorithm runs in quasi-poly time, we believe that the implications for the approximability of several basic optimization problems are interesting.

In Arabidopsis, two floral homeotic genes APETALA2 (AP2) and AGAMOUS (AG) specify the identities of perianth and reproductive organs, respectively, in flower development. The two genes act antagonistically to restrict each other to their proper domains of action within the floral meristem. In addition to AG, which antagonizes AP2, miR172, a microRNA, serves as a negative regulator of AP2. In this study, we showed that AG and miR172 have distinct functions in flower development and that they largely act independently in the negative regulation of AP2. We uncovered functions of miR172-mediated repression of AP2 in the regulation of floral stem cells and in the delineation of the expression domain of another class of floral homeotic genes. Given the antiquity of miR172 in land plants, our findings have implications for the recruitment of a microRNA in the building of a flower in evolution.

Convolutional codes of any rate and any constraint length give rise to a sequence of quasi-cyclic codes. Conversely, any quasi-cyclic code may be convolutionally encoded. Among the quasi-cyclic codes are the quadratic residue codes, Reed–Solomon codes and optimal BCH codes. The constraint length K for the convolutional encoding of many of these codes (Golay, (48, 24) OR, etc.) turns out to be surprisingly small. Thus using the soft decoding techniques for convolutional decoding we now have a new maximum likelihood decoding algorithm for many block codes. Conversely an optimal quasi-cyclic code will yield a convolutional encoding with optimal local properties and therefore with good infinite convolutional coding properties.

We consider a general fingerprinting problem of digital data under which coalitions of users can alter or erase some bits in their copies in order to create an illegal copy. Each user is assigned a fingerprint which is a word in a fingerprinting code of size M (the total number of users) and length n. We present binary fingerprinting codes secure against size-t coalitions which enable the distributor (decoder) to recover at least one of the users from the coalition with probability of error exp(-/spl Omega/(n)) for M=exp(/spl Omega/(n)). This is an improvement over the best known schemes that provide the error probability no better than exp(-/spl Omega/(n/sup 1/2/)) and for this probability support at most exp(O(n/sup 1/2/)) users. The construction complexity of codes is polynomial in n. We also present versions of these constructions that afford identification algorithms of complexity poly(n)=polylog(M), improving over the best previously known complexity of /spl Omega/(M). For the case t=2, we construct codes of exponential size with even stronger performance, namely, for which the distributor can either recover both users from the coalition with probability 1-exp(/spl Omega/(n)), or identify one traitor with probability 1.

We present general symmetry arguments that show the appearance of doubly degenerate states protected from external perturbations in a wide class of Hamiltonians. We construct the simplest spin Hamiltonian belonging to this class and study its properties both analytically and numerically. We find that this model generally has a number of low energy modes which might destroy the protection in the thermodynamic limit. These modes are qualitatively different from the usual gapless excitations as their number scales as the linear size (instead of volume) of the system. We show that the Hamiltonians with this symmetry can be physically implemented in Josephson junction arrays and that in these arrays one can eliminate the low energy modes with a proper boundary condition. We argue that these arrays provide fault tolerant quantum bits. Further we show that the simplest spin model with this symmetry can be mapped to a very special ${\mathbb{Z}}_{2}$ Chern-Simons model on the square lattice. We argue that appearance of the low energy modes and the protected degeneracy is a natural property of lattice Chern-Simons theories. Finally, we discuss a general formalism for the construction of discrete Chern-Simons theories on a lattice.

In project scheduling, a set of precedence-constrained jobs has to be scheduled so as to minimize a given objective. In resource-constrained project scheduling, the jobs additionally compete for scarce resources. Due to its universality, the latter problem has a variety of applications in manufacturing, production planning, project management, and elsewhere. It is one of the most intractable problems in operations research, and has therefore become a popular playground for the latest optimization techniques, including virtually all local search paradigms. We show that a somewhat more classical mathematical programming approach leads to both competitive feasible solutions and strong lower bounds, within reasonable computation times. The basic ingredients of our approach are the Lagrangian relaxation of a time-indexed integer programming formulation and relaxation-based list scheduling, enriched with a useful idea from recent approximation algorithms for machine scheduling problems. The efficiency of the algorithm results from the insight that the relaxed problem can be solved by computing a minimum cut in an appropriately defined directed graph. Our computational study covers different types of resource-constrained project scheduling problems, based on several notoriously hard test sets, including practical problem instances from chemical production planning.